Diana had 45 as many coins as Jane. The sum of the number of coins Diana and Jane had was the same as the number of coins that Gem had. After trading, Gem gave 30% of her coins to Diana and received 10% of Jane's coins. After that, Jane continued to trade and increased her number of coins in the end by 20%, find the ratio of her number of coins to the sum of Diana's and Gem's coins in the end.
| |
Diana |
Gem |
Jane |
Total |
| Before |
4 u |
9 u |
5 u |
18 u |
| Change 1 |
+ 2.7 u |
- 2.7 u |
|
|
| Change 2 |
|
+ 0.5 u |
- 0.5 u |
|
| After 1 |
6.7 u |
6.8 u |
4.5 u |
|
| Change 3 |
- 0.9 u |
+ 0.9 u |
|
| After 2 |
12.6 u |
5.4 u |
18 u |
Total number of coins that Diana and Jane had at first
= 4 u + 5 u
= 9 u
Number of coins that Gem had at first = 9 u
Number of coins that Gem gave to Diana
= 30% x 9 u
=
30100 x 4 u
= 2.7 u
Number of coins that Gem received from Jane
= 10% x 5 u
=
10100 x 5 u
= 0.5 u
Number of coins that Jane increased by when she continued to trade
= 20% x 4.5 u
=
20100 x 4.5 u
= 0.9 u
Number of coins that Diana and Gem had in the end
= 6.7 u + 6.8 u - 0.9 u
= 12.6 u
In the end
Jane : Diana and Gem
5.4 : 12.6
540 : 1260
3 : 7
Answer(s): 3 : 7
